Geodesic
Eigenvectors of the Baxter--Bazhanov--Stroganov $\tau^{(2)}(t_q)$
Teoretičeskaâ i matematičeskaâ fizika, Tome 155 (2008) no. 1, pp. 94-108

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We give explicit formulas for the eigenvectors of the transfer matrix of the Baxter–Bazhanov–Stroganov {(}BBS{\rm)} model {\rm(}$N$-state spin model{)} with fixed-spin boundary conditions. We obtain these formulas from the formulas for the eigenvectors of the periodic BBS model by a limit procedure. The latter formulas were derived in the framework of Sklyanin's method of separation of variables. In the case of fixed-spin boundaries, we solve the corresponding $T$–$Q$ Baxter equations for the functions of separated variables explicitly. As a particular case, we obtain the eigenvectors of the Hamiltonian of the Ising-like $\mathbb{Z}_N$ quantum chain model.
Keywords: integrable quantum chain, fixed boundary conditions, method of separation of variables. 
@article{TMF_2008_155_1_a7,
     author = {N. Z. Iorgov and V. N. Shadura and Yu. V. Tykhyy},
     title = {Eigenvectors of the {Baxter--Bazhanov--Stroganov} $\tau^{(2)}(t_q)$},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {94--108},
     publisher = {mathdoc},
     volume = {155},
     number = {1},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2008_155_1_a7/}
}
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N. Z. Iorgov; V. N. Shadura; Yu. V. Tykhyy. Eigenvectors of the Baxter--Bazhanov--Stroganov $\tau^{(2)}(t_q)$. Teoretičeskaâ i matematičeskaâ fizika, Tome 155 (2008) no. 1, pp. 94-108. http://geodesic.mathdoc.fr/item/TMF_2008_155_1_a7/